Electrical wave filter



1,644,004 t- 4 19.27 o. J. zoBEL ELECTRICAL WAVE FILTER Filed- May 4, 1925 G'Sheets-Sheet 1 AAM I 'f/,JZM/ 333605344 BY M J A TTORNEY 1644004 Ot. 4, 1927. Q. IJ. ZOBEL v v y ELECTRICAL wAvE FILTER Filed May 4, 1925 e sheets-sheet 2 ffy, y 17a/0 I?,

@f ff IN VEN TOR WL l ATTORNEY ELECTRICAL wAvE FILTER Oct. 4:

Fiied May 4, 1925 6 sheets-sheet s w24 f'y. 25 j;

Zw C/fx l f y 0 j?,

IN VEN TUR 0. JZnel BY A TTORNEY Oct.. 4,1927. 1,644,004

O. J. zoBEL.

ELECTRIGAL wAvE FILTER Filed May 4. 192:5 s sheets-sheet .4

L L, vf y Y IN VEN TOR 1,644,004 Oct. 4, 1927. o' J ZOBEL ELECTRICAL WAVE FILTER Filed Maty 4. 192s s sheets-sheet 5 I N VEN TOR l 0. JZM/ A TTORNEY 1644004 ou. 4,1927. o. J. ZOBEL L ELECTRICAL WAVE FILTER Filed May 4. 1923 e sheets-sheet s Z] L a@ GZ] .l M l /ZQJ 0 g C AMAA AMM o @my l 1%@` IN VEN TOR ATTORNEY Patented Oct. 4, 1927..

UNITED STATES PATENT OFFICE.

OTTO J. 'ZOBEL OF NEW YORK, N. Y., ASSIGNOR T0 AMERICAN TELEPHONE ANDTELE- GRAPH COMPANY, A CORPORATION OF NEW YORK.

ELECTRICAL WAVE FILTER.

Application led May 4, 1923. Serial No. 636,668.

The principal object of my invention is to provide a new and improved network for the diversion of alternating electric currents into different branch circuits in accordance with their frequency. Another object of my invention is to provide a wave-filter of lowand-band pass class. Another object is to provide awave-ilter of this class with means for adjustment or modification so that wavefilters of all other desirable useful classes may -be obtained therefrom. vAnother object is to provide methods of adjustment by `which a wave-filter of the class mentioned can be made to serve for a variety of uses.

All these and other objects of my invention will be made apparent in connection with the following specification in which I have disclosed a limited number of s )ecific embodiments of the'invention. The following specication will relate tothese examples with the understanding that the invention is defined' in the appended claims.-

Referring to the drawings, Figure 1 is a general diagram of a ladder-type wavefilter. Fig. 2 is a diagram showing certain particular? embodiments for the impedances a, and z2 of Fig. 1. Fig. 3 is an attenuation-frequency diagram for the wave-filter defined asin Fig. 2. Figs. 4 and 5 are diagrams each showing a set of cert-ain generalized values for the' impedances ai' and 22 of Fig. las compared with the values in Fig. 2. Fig. 5 is an attenuation-frequency diagram for the `Wave-flter defined as in Fig. 4 or Fig. 5. Fig. 6 is an impedance frequency diagram fora ladder-type wavefilter made up as in Figs. 4 and 5 respectively. 'Figs.'7 and 8 arediagrams of adjustable wave-filters built u on the plan of Figs. 4 and 5 respectively. igs. 9, 12, 15,18, 21, 24, 27, 29,33 and 36 are dia rams for the series and shunt impedances o special case wavefilters that may be derived from Fig. 7 by certain particular adjustments of its elements. Figs. 10, 13, 16,19, 22, 25, 27, 30, 34 and 37 are diagrams for the series and shunt impedances of special case Wave-filters that may be derived from Fig. 8 by certain particular adjustments of its elements. (Fig. 27 is included in both lists for a reason that f will be pointed out presently.) Figs. 11, 14, 17,. 2o, 23, 26,- 28, 31, 32, a5 and 38 am attenuation frequency diagrams for the wave-filters defined in accordance with the respectively associated impedance element diagrams in the drawings. Figs. 39 to 42 are diagrams illustrating equivalent wave-filter structures obtained by means of the deltastar or star-delta substitution. Fig. 43 shows a transformer substitution as compared with Figs. 41 or 42. Figs. 44 to 49 are diagrams of pairs of equivalent networks.

Referring to the ladder-type wave-filter shown in Fig. 1, this is a recurrent network with successive series impedances a, and alternately disposed lshunt impedances z2. The input terminals of the networks are at 1, 2'. In developing the theory of such a network, it is convenient and is a well recognized practice first to assume that it extends infinitely from the terminals 1, 2. The theory 0btained on this basis will then be found useful with simple modifications when the switches 3, 4 are thrownl so as to terminate the network by an appropriate impedance Zh. It is also assumed'that the impedances al and a, are pure reactances. YIn practice it is generally desirable that they shall have as little dissipation loss as practicable, and it is possible actually to construct the coils and condensers of a, and z2 so that the wavefilter will approximate closely in its per. formance to the ideal wave-filter with dissi pationless elements. When alternating electromotive forces of a certain fre uency from the generator G are applied t rough the initial'impedance Z., the resulting currents entering the network will, in general, divide to the series and shunt paths of the network. When the impedancesz1 and z, are appropriately designed, the `currents enterin the network at 1, 2 will be shunted in E'arg'e part for certain fre uencies, in which case the currents are sai to be attenuated, but the currents will not be shunted substantially for other frequencies, in which case they are said'to be passed.

The wave-filter shown in Fig. l has midseries initial termination at 1, 2; this means that the network begins with half a full series impedance as is indicated on the. drawing. The impedance K1 across the points 1, 2 is called the mid-series characteristic impedance, assuming the infinite extension of the network to the right as already enplained. Evidently "his impedance will be the same across any pair of mid-series points such as 1', 2. The section between 2 and l', 2 is called a mid-series section.

The shunt element between the points 5, (i is replaced by two impedances each of Value 222; it will be evident that the impedance value of these two impedances in parallel is z2. The impedance to the right across the points 5, 6, represented by K is called the mid-shunt characteristic impedance, and the section between 5, 6 and 5', 6 is called a mid-shunt section The propagation constant oi the network of Fig. 1 represented by the character I", is defined to be such a number that e*" equals the ratio of the current in 'any series element e, to the current in the next preceding element-.e1 nearer to the input terminals l, 2. F is, in general, a com lex number;

let its components be given y the equation constant and B the hase constant. (i) The following forma se may be readily proved for Fig.. l.,

la mehr-.Hm

The foregoing formulae are valid for a ladder-type Wavedilter in which the imped-A ances e, and e, take any form Whatever. For the let z, ta e t 1e forni designated 21k in Fig. 2,

where R is a positive real number.

The frequency of intinite attenuation, fm, is

determined'by the assignment of values toI the critical frequencies fo,

,and Attention is directed` fr f2 to Fig. t which ur ose of the present specificatiom,

nee-enea A wave-filter constructed. in accordance with Fig. 2, will be an example of a conetant It Wave-Elton A constant k 'Waveilter is deined to be onefor which lefk2 Where ic, the oharacteristi yimpedance of the corresponding smooth line, is a constant. ltk can readily' be shown that thus establishing that=R `for Fig. 2, and that a Wave-ilter made l'according to the plan of Fig. 2 will be a constant is Waveiilter.,

By means of (la), the attenuation-trequency characteristic oi? the Wave-lter of Fig. 1 may be obtained, when the values of e, and e, are known. For the values given in Fig.` 2, this characteristic is given in Fig. 3. It will be seen that from zero frequency up to fo the currents applied at l, 2 in Fig. lA are transmitted Without attenua tion. For frequencies from f, on up to f1 the currents are attenuated and at one par ticular frequency, fm, Within this attenua-e tion band, the attenuationbecomes innite. Again, from frequency on up to f2 the currents are transmitte without attenuation, and from 2 up to infinity they are again attenuate -With innitel attenuation at the' upper extreme, that is at infinite frequency. p

rlihe critical frequencies fo, ff and f2 are the frequencies at which zlktakes the re`v spective values +i2R, -z2lt and -l-z'2R. The general value of eik is given by the following equation: p

Bly assigning to .21K each of the three values given above corresponding to the three critical values of f, We have three equations which, we may solve with respect to fo, f, and .f2 as parameters. In this Way We can desi n the wave-filter so as to putthe criticai y'rcatpiencies fo, f1 and f2 atan points` we -lease along the frequency sca` e. The resutin equations of design" in 'terms of f, f, and 2, are as foilows': l

shows another set of valuesy for the impedm ances z, and ze. Itis now roposed to .re-I place el of Fig. i by 2 of IBig. 4 and z2 of Fig. l by e2, of Fig., 4. L11., C and r have the same values as 1n Fig. 2; m1 and ma arey two arbitrary parameters; and the values of a, b, e, al, e and f are reached asfollows:

Impo'se the condition vthat the mid-series characteristic impedance is the same for Figs. v2 and 4, that is,

i K1k==K11 (11) From (3), (6) and (11), it. follows that:

Z:i:F(a'a ba C: di en f7 Lika G1R); (13) in cach ofl (12) and (13) the impedance 2. can be expressed as a function of the reactances 2m-)11k and I 1 I 2T fc' 1k Since these expressions of (12) and (13) must be equal atl all frequencies, We'may equate the coefiicients of like powers and products` of these reactances, and thus We shall get siX equations, determining a, b, c, d, e and f in terms of m1, m2, fo, f1 and f2.

But in ordinary practical design we' are not prepared to assign values to m1 and m2 at the outset. We have seen that for' Fig. 2 We can assign the three critical frequencies fo, f, and f2 at the outset and thereupon the design of the constant le Wave-filter becomes determined by (8), (9) and (10). The wave-filter of Fig. .4 is not a constant rameters m, and m2.

which itm'ill be seen that the abruptness of the cut-olf at a critical frequency may be increased if we can bring the frequency of ininite attenua-tion close to the cut-off frequency. This suggests that it will be advantageous in Connection with Fig. 4 to assign two frequencies of infinite attenuation, one in each attenuating band. The three frequencies of infinite attenuation 1" 1. f1.. andfg iu Fig. 5a 'are respectively the resonant frequencies of the simple shunt branch in Fig. 4, with which are associated the coefiicients e and jl a and c and By assigning the resonant frequency of such a branch it is easily shown thatthe product of the coeiicient is made definite, and in this way the equations are obtained.

@ fofifz Twin-aware 14) C fofifz (15) Hencein addition to the critical frequencies fo, f, and f2, We assign as definite values at the outset the two frequencies of infinite attenuation fla, and f2s. vThese five parameters determine the design of the filter of Fig. 4. vIts equations of design are (8), (9), (10), (5) and the following eight equations 16) to (23), in which g and h are certain functions of the variable fs as given by equations (24) and (25):

lc filter. Compared With the Wave-filter of -Lgqqb Fig. 2, it"has two additional arbitrary pam1=f 2m (16) Its attenuation-fre- 1 E quency characteristic is given in Fig. 5, from y y fzz (me bfi) t fi- Jltl fp )h f2s fa g flfzfa fz (17) [(1 n+n n fitn) n][l fs f1 f2 fz@ fz fzz where and 1%/ agyago (i. (25)' vIn 'obtaining the foregoing equations it will also be found incidentally that the remaining dependent frequency of infinite attenuation is determined -as follows:

' in the manner illustrated by the example of Figs. 2 and 4. The element z, in the equivalent filter will have a plurality of parallel simple resonant paths, their number being the same as the number 'of reactancc elements in el. :All mid-series equivalent Wavefilters including their prototype (for which m1=m2:. .:1) have the same midseries characteristic impedance at all frequencies, and the same critical frequencies,

but not the same attenuation characteristics. The presence of the extra parameters, the

ms, enables us to adaptthe design to givey a desired attenuation-frequency characteristic.

Attention is ldirected. to Fig. 5, which shows another set of special values for a, and .z2 of Fig. l. )Vhereas the design of Fig. 4 was made definite by imposing certain conditions, among which was the condition that its .mid-series characteristic impedance should be the same as for Fig. 2, on the other hand the design of Fig. 5 is made definite by assuming that its mid-shunt characteristic impedance is equal tothe mid-shunt characteristic impedance ofthe Wave-filter of Fig. 2, and its propagation constant the same as that of Fig. 4. In view of thc cxpo'sition that has been given for Fig. 4, it will not be necessary to give the corresponding demonstration for Fig. 5. The result is that with the system of lettering employed in Fig. 5 the'sanie de sign equations serve as for Fig. 4, viz, (8), (9),l (10), 5) and (16) to (23).` a

Moreover, mid-series equivalent sections or mid-shunt equivalent sections or both can be combined in one and the same wave-filter, for the impedance characteristic will not be affected andthe critical or cut-off made to give a favorablefattenuation characteristic over a Wide frequency range.

In Fig. 6 the mid-series characteristlc 1mpedance and the mid-shunt character1st1c 1mpedance of the respective wave-filters of,

Figs. 4 and 5 are shown as functions of frequency. These are plotted bythe aid of and (4). From (2) it follows that in the passbands the impe-dance is apure resistance and in the attenuating bandsit isa pure reactance. In Fig. 6 only the resistance values (for-the pass bands) are shown.

When a wave-filter is connected with a smooth line, it may be desirable that its impedance shall be as nearly as practicable the same as that of the smooth line, especially over the pass bands. It will be seen from Fig. 6 that in each pass band the impedance touches they resistance valueR as a maximum or minimum according as the `wave-'filter is of the structure of Fig. 4 or Fig. 5.v By the proper design of the terminal impedances Za and Zh, the resistance can be approximated to R much more closely than in Fig.

'6, and the value assigned to lR at the'outset may be the characteristic impedance (resistance)of the smooth line.

In Fig. 7 I have shown a wave-filter with the filter elements of Fig. 4 and with facility for adjustment `of its impedance elements, and similarly in Fig. 8 a Wave-filter with the elements of Fig. 5 is shown with facility for adjustment. l#

Accordingly, with either of the Wave-filters of Figs. 7 and 8 we-can assign any values we please to the five parameters in order of magnitude fo, fw, f1, f2 and f2s. Then with the aid of (8), (9) (16) to (25) we can get values for all the inductances and capacities in each Wave-filter of Figs. 7 and 8 and adjust those inductancesand capacities accordingly. Thereupon We shall have a Wave-filter that will give the pass bands and attenuation bands defined by fo, f1 and f2 and that shall have thesharpness of cut-off determined by the location along the frequency scale of` f1... and f2...

By giving certain special values to the fs atthe outset or by lmaking certain `of these values coincide, and by making adjustments of the capacities and induct-ances in accordance with the design equations based on such special values of the fs, a Wide variety` of comparatively simple special wave-filters may be obtained. Some of these will now be pointed out in brief outline.

1. Low pass wa/ve-fZters.-Let

The corresponding simplified forms taken 1 (lo), (5) and i tei-istie is shown.

lns

If, in addition jg.=, the wave-filter becomes of` constant le The formulae for Fig. 9 are where The horizontal dotted line in Fig. 11 indicates that as the frequency increases without 5. Low-amZ-u'gh pass-(or band stop) The corresponding structures are shown in Figs. 15 and 16 -and the attenuation-frequency characteristic in Fig. 17. If, in addition, we make it follows that f1.=f1., and the wave-filter becomes of constant k type.

limitthe corresponding attenuation ap- The formulae for Fig 15 are proaches a finite value which is the ordinate I L :mL/1k Lz,-v 'Ln C.: C u., of the dotted line; in other Words the curve l l m is 'asymptotic to the line A=A. Where A C, k C, is a finite value taken by A Whenf= C2= b, L,=eLzk, C'z fi" The significance of the dotted line is the same in Figs. 2o, 23, 31, 32 and 35. 1nd for F1g-16 y f2. High pass wave-jlterss-Let L Eg La: L! C :die

` j0=o and j2=f2= (28) g b m y The corresponding physical structures are C2=m()'m Li'xaLj", C'ize'cm shown in Figs. 12 and 13 and the correspondf c ing attenuztion-frequency characlerijstic in vwhere y Fig. 14. I in addition we ma. e 1.=0 the wave-filter becomes of7 constant k type. L,kE[rL,x]= (f1 )R Ln= --1-- The formulae for Fig. 12 are 1 Tff1 41.(1-19) l 0 c= L2= 2,?, CF C 4*fm-fe C EVC mi I and for Fig. is 1 -f-L) 1 m) mmsbfm LzI- k Qm 14:92, 1

l b y l m I m y j! ,Jemig il( 121.1):[4 f1-f)']= f E "1 ffm m fam t fof1 -f 1),: @U1-fell 1 (1+fg 4e(f1fo)]5ef mf of 1 m 'fof ffofi j, and for Fig. 19 .v L: Lm 4t Bam?? 'lmfve-temr-Let L1: El L2 E Clacm ffii. ce' im l, The corresponing structures are shown in- Cf'miolx, L1a d, C 1:00a lfigs. 1 19 and the attenuation-frequency characteristic Fig.,20. where The ormuisc 'er Fig. 18 are f Cn L ==7R L Mm-Lm, L1=m1Lim L2=IL1M C1 u 1f( n- 1)' n I 4lf1f2 m2 C t, C ,f2-fx 1 02s i LfcL Cf: ag C LTER' C ,rm-fon www mlm

igloo im f2.0 gfzlw hoyo@ dz! o www... 1 fnl. ihfif 22m H m1=m2=m, wc haw@ the M-type, and

fllwfz :flfm mld 9:51-

Various simple? forms of band pass Wav@- lters can 'be obtained by some sacrico in oxibility of o'osign as compared *with Fis. 18, 19 and 20; some of these Wil now c indicated. y

4?. Bami pass wwefilters of thonee elements per section-#ln addition to 'cho condition expressed by ict The corresponding structures orc shown im f C fil-foo Alternatively to the "oicgoing, in oddiiiom io 'tho condition of (30), ici;

fluo :fh 31nd. fg D@ The corcspondimg structures and michoasion diogi'om oro shown m gs. 24, 25 and 26 coopoctwoiy.,

l im @$53352 @om Q m 2k WUV'QR 4b. ,Band pacs wave-filters with fom" elemegis per sceicco-iin adition to the comdition of (30), ict v fl 03 and f2s: The corresponding stiuctiiro "will be of constamt lo Wpc, Where c=R and ihoio will' Foo one example.. Tho structuro is @hmm in Fig. 27, and its' ottonuation-re ucmoj;V

oimmotciistic is given in ig. 28. T o dosign' *formaba or@ Y o Aitormtivciyjo bho foregoing, in "oddioion izo Kcho condition of (3Q), ict

fam-:fo (35) v Tine corresponding siruciurcs siro shown in F1guics-29 :and 30 ond the corresponding tenuatl'on-rcqucncy choractoristc in lig.

The ormui for Fig. 29 Saffo i where Llk, 01k, L2., and C21. are given by (34) and where mi trimm Vm2:

As a further. alternative, in addition to the condition of let The corresponding structures will also be shown by Figs. 29 and 30, and the attenuation-frequency characteristic -will be given by Fig. 32.

ml: i f2.0.

4. Band pasarY wafve-ylters ham'ng f/ve p elements 'per section-In addition tol the condition of (30), let

fb o.

YAlternatively to the foregoing, in addition .to the condition of (30), let

The corresponding'structures are shown in Figs. 36 and 37- and the `.attenuation-frequency characteristic in Fig. 38.

The formulae for Figs. 29 and 30 'are (36) s The formulae for Fig. 36 are d L1 :Lm L2 5L,

Where and where Llk, C11., L21, and C21. are gi'ven by In the wave'ilters of the present disclosure it will be evident that various equivalent substitutions of groups of elements may be made. For one example, the deltastar or star-delta transformation may be made. As a simpleillustration, consider the wave-filter of Fig. 39 which has the impedance elements of Fig. 24, each series condenser of Fig. 24 being replaced by. an equivalent pair of condensers in series. At each point such as 7 in Fi 39, there are three star-connected capacities. In Fig. 40 these are replaced by the three delta-connected capacities forming the mesh 7'# Again the elements of Fig. 21 give the Waveiilter of Fig. 41 with three star-connected inductances at 8. InFig. 42 these are replaced by the three delta-connected inductancesforming the mesh 8". By an alternative step, winding the coils 9. and 10 on the same core as in Fig. 43, with pro er self and mutual inductances, an equiva ent for Figs. 41 or 42 is obtained.

Other substitutions than star-delta and delta-star maybe made, and sometimes the will be very convenient, in accordance with' Figs. 44 to 49. The two networks of Fig. 44 are equivalent when The two net works of Fig. 45 vare equivaient when I The two networks of Fig. 46 ere equivalent emi-ee. emr-ine, e:

These sixceses of equivalence of networks ere reediiy preveoi by ectueiiy working out fix@ the impedance velues im each cese. For exsimple m Fi f. fi-i the lmpedence o'i the upper meer/:leek is given by the expremoili `eicel the impedance oil? beio'wer network is given by expression:

Substituting for e eiid i iri terms of in accordance with (4r-1)' this impedence expression for the lower metworkbi Fig. ifi will reduce to' eil identity witirtbe impedance expression for the upper rreiwo1k,'thus provthe equivalence of tbe two networks et eli iiequencies. in e similar meneer ehe equivalence iii eecb ci? Figs. 45 to 49 may be established.

ii cieim: v

l. A icw-eird-bcriri pese weve-lter bev ing mid, section. equivelerice with e. cons'teinrJ is. weve-iiiiei'l end comprising ineens io pro-- duce inoiie eteenuetiori et iwo dibierene frequencies between eiieposs reeges ci' fre-- quericy emi. ineens to produce iniiiiae et tenuetiori et one frequency ebeve bhe bandi pese range ci frequency.

2. A low-end-bemi weveiiier of iedcier iype bevirig mid section equivalence wih e. given proioeype weve-iiiter emi corri-= prisiog means to produce irifiniie etienne-s inioii et two different frequencies between the pese ranges of frequency end meens to produce infinite attenuation ei; one frequency above the bend pese range of frequencyD seid progoi-ype weve-fiber. bevirlg series and shunt. reeeieiice coriibiiieri-ions9 eecb series combine.- iioii consisting oi L11. in series with the pereiiei combmetion of @Lik and @Ik ami exi-cb sbarre combineiioii consisting of C21. iii. pereiiei wib. L2 :mii TCM the ies; two eiereeiis in seriess where the Lie eed tbe Cs eo. +a) @+1,52

The two networks of Fig. 48 are equivalent when The two networks of Fig. 49 ere'equivelent' when f 4 bo. Lem +15),D e2 *einem i R being e .positive reel number.

3. A sectionei leder type low-and-bencipass weve-filter comprising et ieest nine ed .Justebie reeciences per complete section whereby its `ibree criiziceifrequencies endl twoirequencies oi' iuiniteetiemietiom may be put ai; any consistent veines desired.

4. A. secticrlei ledder sype iow-erid-benoi pass wave-filter comprising et least nine ed.- justable reectences per compiete section whereby it may beedjusted alternatively to serve es e low pass-lter or e high ess-iizer, gli e low-end-high pass iiiter or eliemi pees ter.

5. A low-end-bend pees weve-filter with riine reectarice elements per section end. with means to cut ou?J 'certain of these elements whereby the weve-filter will become o iow' pass, high `:bess9 low-enfi-iiigh .pees or band poss weve-lter according to which elements erecut oui.

6. A iow-arici-beiid pese weve-lter wich e, plureiity of reeczarice eiemens er section end with means to cut olii*l certain of these elements whereby the weve-fiber will become e. iow pees5 high peses iow-en i-bigb pass, or bend. pass weve-lter according to which eiemeris ere cui our..

7. A bend pass wnve-fiiier coiiiprisng series emi shunt reectances and comprising ineens to produce infinite attenuation et iwo different frequencies, one in eecb. efutenuetiiig range ori respective sides of the pass bend.

8. A.. bend pass weve-iiler comprising means to produce infinite etteriueiion er eecb of two critical frequencies, one in eecb ottenueting range on respeciive sides of tbe poss bend end bevirig its reectence eieirients ejueaebie whereby its two cuit-off frey qeeiicies eiifi its iwe frequencies of innii/e sstent values.

9. A Iow-and-ban'd pass wave-filter of -ladder typehaving three like inductencecapacity combinations in each section, these three combinations each being related alike to the rest of the section, whereby the l ter may be adjusted to give infinite attenuation at several desired frequencies in its attenuation ranges without disturbance of its cut-0E l0 frequencles or its impedance-frequency characteristic.

In testimony whereof, I have srined myl name to this specification this 3 day of May, 1923. O'ITO J. ZOBEL.- 

